How Does Quantum Mechanics Combine Particle and Wave Descriptions?

[zbyszek]

Obviously, you are using circular arguments.

Could you be more specific? I mean, list the arguments and show that they are circular?

J. von Neumann did work simpler. He postulated the reduction phenomenon and developed the theory of measurements under assumption that the statistical interpretation is correct. J. von Neumann was outstanding mathematician and physicist. He honestly pointed out that these two assumptions lead him to absurd.

Did it lead him to a contradiction? If that it is what you mean, which of the premisses
is invalid?

When we discuss the A.Tonomura results you simply refuse to accept what you see right in front of your eyes. When I started to study physics I never dreamed that I will see such a picture. You see properly amplified image of the single electron. And it is most beautiful picture I ever seen. It is highly regular. One may describe it completely using only three parameters. Apparently, it has nothing to do with statistic. No room for the mystery at all.

Anonym, you act as if you knew something I still don't. If that is really so, I honestly
would love learning it.
Could you guide me to the enlighment, please? I am serious.

From descriptions of the Tonomura experiment, electrons pass the double slit setup, one electron at the time, and their position is recorded some distance from the slits. All electrons are prepared the same way. One electron produces one spot. Many spots
group into interference fringes.
Are we talking about the same experiment, at least?

The reduction of wave packet can’t be accepted as a postulate. In general, the postulate must be simple, clear, self-obvious and universally valid. The reduction is not simple, clear and by no means self-obvious. Most importantly, it is the inherent property of the QM mathematical formalism. Since the measurement instruments are macroscopic, it therefore have to have natural explanation within the classical physics. And it does not. Therefore, the classical physics is not complete. But this is a trivial statement. Until now nobody explain the wave mechanical nature of HJ formulation, which allow to formulate the most important principle postulate of the physics:
Principle of Least Action. Without that explanation all of the classical physics has no foundation.

Here, I don't know what you are talking about.
First, I don't need the reduction postulate and never did.
Second, how come "it is the inherent property of QM". I have never seen a wave
packet reduced in QM calculations. I have seen only unitary evolutions.
Third, is it possible to talk QM without solving all shortcomings of the classical mechanics?
One theory at the time, please!

Cheers!

 

[reilly]

Of course it exists. Nothing stops you to perform a fully QM treatment of the entire experimental setup except the lack of a good enough computer.



Classical world is quantum world.



In a double slit experiment it's the wall with the slits. An electron passing near such an object changes momentum. The mechanism behind this change is ignored so we shouldn't expect a good prediction of the individual detection event. So, besides the probable statistical character of the wavefunction itself, we have another approximation regarding the potential at the slits (which is assumed to be 0 although it's only 0 on average).

.........
Yes, but. You suggest that the wall and slit boundaries have an important dynamical role in the double slit experiment. That's not so clear. Don't see many backscattered electrons from the slits.

Look at the physics: as an electron goes through a slit, it forces electrons in the wall away from the slit boundary. Both the electrons and nucleii are subject to thermal bouncing about. In my view, this is suficient to say that 1. the forces on a passing electron are small ( left balances right), and 2. average to zero over all but the shortest of times.

A somewhat more sophisticated approach is to treat the wall as composed of
nuclear-electron dipoles, which in turn are created by the fields of the passing electrons. This approach makes the handling of magnetism a bit easier.

The translation into QM is to get the "actual" potential seen by a passing electron, and include this in the Schrodinger Eq. (Not to worry about feedback of forces in this problem). Also a helpful fact: the dwell time of an electron in the wall's potential will generally be quite short.

Regards,
Reilly Atkinson

 

[reilly]

zbyszek:Why not? One can control how many electrons enter a double slit experiment. It can be just one. If 1000 revelators click simultaneously that would mean that the electron is apporprieatelly spread (like its wave function ? ."
Why simultaneously? And 70000 will give you better image.
"No one has seen such wonder yet."
A.Tonomura et al. and P.A.M.Dirac in Principles explained it some 70 years ago.

zbyszek:"There is no difference. Repeated observations, as you stated above, is just another name for the observation of the ensemble.

I know that in microscopic (as oposed to statistical) theories I can predict, given initial conditions, with a certainty an outcome of a single run of an experiment. Clearly QM does not qualify as microscopic in that sense. If it did, results of the single runs would be no mystery.

All of this is to point out that no one justified, so far, that a wave function can be viewed as a description an individual quantum object. Thus, it is save to say that we have no theory for these objects."

Sorry,I do not understand your answer. Formulated differently, my question was: what are the interconnection between classical statistical mechanics, quantum statistical mechanics and statistical interpretation of QM or in more compact way: What is the wave packet description?

A. Einstein in his 1928 discussion presented breaf summary of that problem. Today one can say something new?

...

The connection between repeated measurements and ensembles only works for ergodic systems.

However, it is a frequent assumption in physics, and statistics, not unrelated to the often used idea that distributions are Gaussian's.

Here's a simple fact: in this real world of ours we can't predict anything with certainty. Measurement error is a fact of Nature. Thus everything is uncertain, to a greater or lesser degree. Brownian motion occurs in 'classical systems'. That means, of course, that there is no theory of certain events.

That's why we use in experiments the largest sample possible so as to get info about the distribution of measurements with as much accuracy as possible. There are lot's of things that are virtually certain: a gallon of gas in New York is the same as a Boston gallon. The price of gas is another matter: there's virtually no way at present to say what you will pay for your next fill-up.



So, if that's so, why do you single out QM for having a problem that is virtually a universal one?

Regards,
Reilly Atkinson

 

[Demystifier]

And honestly, I have difficulties believing that you can formulate the particle dynamics in a relativistically invariant way. If you can do that, I'll become a bohmian too

I already gave a link, but here it is again:
http://arxiv.org/abs/quant-ph/0406173

 

[vanesch]

I already gave a link, but here it is again:
http://arxiv.org/abs/quant-ph/0406173

Yes, and I responded to that too: you consider free particles, and then introduce the "n-particle wave function" as the n-point correlation function of the free theory, which is a tensor product of solutions of the free KG equation.

But you know very well that once you introduce interactions, that you cannot do that anymore (otherwise, standard QFT would be really easy to solve !).

So of course you can solve for particle trajectories in this free situation, because they all correspond to free world lines of point particles, and you can formulate all that in a relativistically invariant way. But the devil is in the interactions (as is the case in standard QFT too).

There is no simple set of partial differential equations for an "n-particle wavefunction" in this case. So this paper proves nothing in my eyes. It only indicates that a free field theory can have a lorentz-invariant particle trajectory interpretation.

 

[Demystifier]

Vanesch, you are right. But I have also studied the interacting case in
http://arxiv.org/abs/quant-ph/0208185
http://arxiv.org/abs/quant-ph/0302152
Things can be done at least in principle. Unfortunately, you will notice that the interactions are not treated covariantly. Instead, it seems that a preferred coordinate frame is needed. In another paper
http://arxiv.org/abs/hep-th/0601027
I propose that the preferred frame is picked up in a covariant dynamical way. Of course, you may argue that all these theoretical constructs are somewhat artificial and make the theory less elegant. I certainly agree with that, but the results demonstrate that it is not impossible to construct a theory that works, even if it is not very simple. I also try to construct a simpler theory too.

 

[Anonym]

Zbyszek:” One cannot dislike things one understands. I just seriously doubt its usefulness”

“Could you be more specific? I mean, list the arguments and show that they are circular?”

“Here, I don't know what you are talking about.
First, I don't need the reduction postulate and never did.
Second, how come "it is the inherent property of QM". I have never seen a wave packet reduced in QM calculations. I have seen only unitary evolutions.
Third, is it possible to talk QM without solving all shortcomings of the classical mechanics?
One theory at the time, please!”


1.I referred to classical paper by H.D.Zeh for example (Foundations of Physics 1,69 (1970). You may find more in QT and Measurement edited by J.A. Wheeler and W.H.Zurek
2.Spectral Decomposition Theorem. Wave packet is not observable. You may see only indirectly that system is in the pure state.
3.I do not act. I present (I hope consistently) so called “Orthodox QM (quant-ph/0004077).
4.I was involved into discussion of statistical interpretation. Really it is not interested me.” I just seriously doubt its usefulness”.
5.What I try to understand here is whether the coherent state provide the adequate description of the Newtonian “ball” used in classical statistical mechanics and if it is so how to make this basis orthonormal as it should be (J.v.Neumann, Zs.f.Phys.,57,30(1929).

“Anonym, you act as if you knew something I still don't. If that is really so, I honestly would love learning it.
Could you guide me to the enlighment, please? I am serious.”

Sometimes your way to express yourself disturb me. If you already know and understand everything, I can’t help you.
Perhaps, I can tell you something different, some way that you did not consider before. If you are interested, I will send you private message.

 

[ueit]

By that I imagine you mean 3 space + 1 time dimension. This is incorrect. It comes from Hamiltonian phase space.

You forget that there are elements of Q.M. that have absolutely no classical analogue. e.g. spin degrees of freedom. What are the "position co-ordinates" of that?

If you feel that the Q.M. is not defined on an abstract Hilbert space, then you are not talking about standard quantum mechanics here, you are talking about something else.

One should distinguish between what QM is about, its ontology, and the mathematical tools used to describe that ontology.

In classical mechanics, we can use Hamilton's equations or Newton's laws. Still, the theory describes the same thing, say the motion of a pendulum. We don't say that we have a theory describing an abstract phase space.

So, QM certainly uses an abstract Hilbert space, but the theory describes quantum systems existing in space and evolving in time. What do you think is the meaning of time evolution in the absence of spacetime?

 

[ueit]

That means that you assume a ground state, or any other specific quantum state.

If you have 2 particles A and B, and I give you the quantum state psi(r1,r2), you can calculate the "quantum force" from BM. But if I don't give you that quantum state, even if you know the positions of A and B, and their velocities, you won't be able to give me the quantum force. You need psi for that. The trick with the molecule is only because you can somehow assume what is its quantum state (probably the ground state of the Hamiltonian, OR a chiral state OR ...).

The universe, as a whole, cannot be in an excited state as no energy can be added to it. So, we can be certain that it is in a ground state.

An excited molecule, on the other hand, is a subsystem, and it is to be expected that a full description cannot be found by just specifying the momenta and position for its particles. It's like asking for the law of motion of a pendulum without giving the gravitational acceleration.

In order to compensate for the lack of knowledge regarding the whole system (universe) of which the molecule is but a part we need psi.

I don't think there is a need of explanation (which would in that case make appeal to other fundamental aspects which would then require an explanation in their turn etc...). It is undeniable that certain degrees of freedom in nature come in sets of 3 real numbers, which give us an impression of space. So be it. I don't think everything has an "explanation", we can already be happy with a description. In how much this is a strict necessity that the "space behind it" is real, I let the formalism decide. And the problem is that there is no existing theory as of today (not BM) which is demonstrated equivalent with QM and which can be defined *entirely* as some extra structure over spacetime (which would then be a "local realistic relativistically invariant equivalent to QM"). BM needs also that hilbert space. QM lives ONLY in that hilbert space.

If I knew, I would be famous. And maybe there is no "reason" to it, it just IS so.

I certainly agree that any theory has to be based on some postulates and it's meaningless to ask it to justify them. However, in the case of MWI, 3D space does not seem to be postulated, it should be a consequence of the theory.

Let's say I accept a universal wavefunction as the ultimate reality. The question is then, how do we get from there to what it seems to be reality for us. Why a hydrogen atom does not look like a "bunch of spin-1/2 systems" to us?

 

[ueit]

Yes, but. You suggest that the wall and slit boundaries have an important dynamical role in the double slit experiment. That's not so clear. Don't see many backscattered electrons from the slits.

Look at the physics: as an electron goes through a slit, it forces electrons in the wall away from the slit boundary. Both the electrons and nucleii are subject to thermal bouncing about. In my view, this is suficient to say that 1. the forces on a passing electron are small ( left balances right), and 2. average to zero over all but the shortest of times.

A somewhat more sophisticated approach is to treat the wall as composed of
nuclear-electron dipoles, which in turn are created by the fields of the passing electrons. This approach makes the handling of magnetism a bit easier.

The translation into QM is to get the "actual" potential seen by a passing electron, and include this in the Schrodinger Eq. (Not to worry about feedback of forces in this problem). Also a helpful fact: the dwell time of an electron in the wall's potential will generally be quite short.

Regards,
Reilly Atkinson

I think there is no doubt that the electron interacts with the slits, otherwise what part of the experiment is responsible for momentum conservation? The source? The detector?

The big question is how the interference fringes appear as a result of those interactions.

Regards,
Andrei Bocan

 

[zbyszek]

1.I referred to classical paper by H.D.Zeh for example (Foundations of Physics 1,69 (1970). You may find more in QT and Measurement edited by J.A. Wheeler and W.H.Zurek

I've read it. As to quality of this paper it is enough to consider the authors classification
of differrent views on the measurement problem in QM. How would you classify the
statistical interpretation of QM (saying that QM does not describe the measurment at all)
according to the classification scheme introduced by Zeh?

[QOUTE=Anonym]
3.I do not act. I present (I hope consistently) so called “Orthodox QM (quant-ph/0004077).
[/QUOTE]

You list the postulates of QM. All of them, but last, after Ballentine. The last one is the "measurement" postulate Eq.(14). Right after that you claim that everybody agrees
with the list. Well, not everybody. If you read Ballentains work more cerfully you would see that
your last postulate is certainly not a part of the statistical approach to QM.
Especially you could profit from the distinction made by Ballentain between the state
preparation and the measurement.

4.I was involved into discussion of statistical interpretation. Really it is not interested me.” I just seriously doubt its usefulness”.

Fair enough. But why are you asking me about those issues if you are not interested?
Am I being interviewed for a job?

5.What I try to understand here is whether the coherent state provide the adequate description of the Newtonian “ball” used in classical statistical mechanics and if it is so how to make this basis orthonormal as it should be (J.v.Neumann, Zs.f.Phys.,57,30(1929).

Don't know the problem.

Sometimes your way to express yourself disturb me. If you already know and understand everything, I can’t help you.
Perhaps, I can tell you something different, some way that you did not consider before. If you are interested, I will send you private message.

Anonym, I try to keep in mind that my brain can be fooled, and that some of the rock solid
foundations of my understanding of QM can be just my misperceptions. Neural networks
have their weaknesses.
Thus, from time to time I recheck all the premises if new evidence shows up.
Our discussion would be one of those occasions. But I have failed to see the new evidence.
I have read very carefully the nice paper by Ballentine, I tryied to understand the Zeh's
view and yours in the preprint, I learned the original work by Tonomura and here is what
I find:
1. I agree with every sentence of the first part of Ballentine's work. The part with hidden
variables is tricky.
2. Zeh didn't have chance to read Ballentine. Otherwise, he might have commented also
on the statistical interpretation.
3. In your work, you give wrong description of Ballentine's paper (section 1.2), you logic
is questionable in the Recapitulation (section 1.6) when it comes to the two alternatives
A and B (you conveniently forget that neither A or B captures the results from Ballentine's work). Namely, there is also C: QM is exact, no need for any reinterpretation, remove the postulate you have added to the Ballentine's list.
4. I didn't see what is so spectacular in the Tonomura's experiment that could have
force someone to take an orthodox point of view on QM.

Did you really read the papers you referred to in the manuscript? I mean the one by Ballentine.
I don't believe you wouldn't understand if you actually read it. Unless, of course, neurons
in your brain make no new connections.

At the moment it looks to me that you have reservations towards the statistical
interpretation because you don't know it.
Or perhaps, my brain is hard wired already and cannot comprehend the obvious.

Thanks for the references! I didn't know them before.

Cheers!

 

[vanesch]

In classical mechanics, we can use Hamilton's equations or Newton's laws. Still, the theory describes the same thing, say the motion of a pendulum. We don't say that we have a theory describing an abstract phase space.

Ah ? I certainly do. I think that Newtonian mechanics (points in 3-dim Euclidean space with forces and so on) and Lagrangian/Hamiltonian mechanics describe different ontologies ! (which are however observationally identical). In other words, when considering Hamiltonian mechanics, I *do* consider that its universe is a 6N dimensional tangent bundle and not a 3-dim Euclidean space, although one can find certainly a 3-dim Euclidean structure in there.

 

[vanesch]

The universe, as a whole, cannot be in an excited state as no energy can be added to it. So, we can be certain that it is in a ground state.

Mmm, that's a pretty dubious statement...

An excited molecule, on the other hand, is a subsystem, and it is to be expected that a full description cannot be found by just specifying the momenta and position for its particles. It's like asking for the law of motion of a pendulum without giving the gravitational acceleration.

In order to compensate for the lack of knowledge regarding the whole system (universe) of which the molecule is but a part we need psi.

You mean that psi is then the summary of the interaction with the rest of the universe ? The "noise that comes from elsewhere" ?

Ok, but I can think of a toy universe just with one molecule in it, and I give it a certain quantum state |psi> which can be just any state (not even a stationary state). Clearly, this is then the "state of the universe" as there isn't anything else around. I can also give you the initial positions and velocities of the electrons and nucleae. And you can STILL not calculate the quantum forces without using psi - nevertheless, there is no "noise coming from elsewhere".

I only say that to show you that in BM, the wavefunction has a life of its own, with its own dynamics, and its own dynamical content which is NOT derivable from the particle positions and velocities elsewhere. As such, it is entirely part of the dynamical description, and hence must have its own ontology in addition to that of the particles.

However, in the case of MWI, 3D space does not seem to be postulated, it should be a consequence of the theory.

MWI is only a way of looking upon a quantum theory, and a quantum theory needs as its inputs the list of the degrees of freedom, the hamiltonian flow, and the link to (subjective) observation. Depending on that, you can put in the 3-dim space rather explicitly (such as is done in non-relativistic quantum mechanics or QFT), or you can hope that it will somehow emerge if you set up a different structure (LQG ?).

Let's say I accept a universal wavefunction as the ultimate reality. The question is then, how do we get from there to what it seems to be reality for us. Why a hydrogen atom does not look like a "bunch of spin-1/2 systems" to us?

That's the entire definition of how we extract subjective experience from the wavefunction ! It's the "shove-it-all-under-the-carpet" part of MWI (but also of GR, to a lesser extend btw). You have to accept that the psycho-physical link is non-trivial, and corresponds to certain subspaces of hilbert space being associated with certain subjective experiences. Which is in any case a to-be-accepted problem for a physical theory ; only, for some physical theories, this aspect "factors out" (like in Newtonian mechanics - but not in Hamiltonian mechanics !) and in others (such as MWI), it forms a crucial part of it.

 

[Anonym]

Zbyszek:” You list the postulates of QM. All of them, but last, after Ballentine. The last one is the "measurement" postulate Eq.(14). Right after that you claim that everybody agrees with the list.”

Sorry, I am not S.L.Adler. It is due to my terrible English.
I only quoted Adler’s paper and I meant the first paragraph “Orthodox QM and Issues it Raises”. I meant that point of view I present somehow close to the orthodox QM. I don’t agree with the presented list of “postulates”. It should be obvious since no one of them fit the description of the requirements for postulate that I wrote to you.

Zbyszek:” But why are you asking me about those issues if you are not interested?”

“Or perhaps you misinterpret wave functions? Does a wave function correspond to a single quantum object or to an ensamble of single quantum objects?

If the second is true then QM has nothing to say about particle or wave character of a single quantum object, a single electron for example. QM describes ensambles.

If the first is true then how come that electrons appear as points on the screen in Young-like experiment although the their wave functions spread across the whole screen? In other words if QM applies to single quantum objects then one should be able to predict WITH CERTAINTY (not just probability) an outcome of a single run of an experiment with one electron!”

I tried to understand why you bring statistics into discussion of the wave packet description. For me it is relevant in the discussion of wave packets description.

Zbyszek:” I mean the one by Ballentine.”

Sorry, I did not. I promise I will.

 

[Anonym]

Reilly:” The connection between repeated measurements and ensembles only works for ergodic systems.

However, it is a frequent assumption in physics, and statistics, not unrelated to the often used idea that distributions are Gaussian's. “

Your argument is very convincing for me. I have no doubt that it should be Gaussian’s. However, adequate means unique. And that what I try to see.

Reilly:”Here's a simple fact: in this real world of ours we can't predict anything with certainty. Measurement error is a fact of Nature. Thus everything is uncertain, to a greater or lesser degree. Brownian motion occurs in 'classical systems'. That means, of course, that there is no theory of certain events.

That's why we use in experiments the largest sample possible so as to get info about the distribution of measurements with as much accuracy as possible.”

All classical theoretical physics: Newtonian mechanics, special relativity,electromagnetism, gravitation and even statistical mechanics are “theory of certain events”.

You consider only one aspect of the problem. Your description of the measurements fit perfectly the mathematical framework used in the classical physics. It essential feature is the use of analysis (classical,vector and tensor consequently). In the foundation of the analysis lies lim operation which can’t be reduced to addition and multiplication. It means intrinsically that for every predefined epsilon > 0 you may find suitable delta > 0. And thus your notion of accuracy fit it perfectly too.
However, QM do not follow that scenario.
Consider properly calibrated and functioning set of the measurement instruments. You perform the observation and obtain a point. Now you repeat the procedure for the identical system (the standard QM treatment of that notion). Your new observation is legal exactly as the previous. However, it do not always satisfy your requirement. Sometimes one obtain points where delta is arbitrary large. This do not mean that now your measurement equipment is spoiled. This mean that you met new physics (and new mathematics consequently).
Quantum world is not a classical world.
Now let me add dual deterministic treatment of the repeatability.
It is not sufficient to perform the measurement only in one laboratory. One need confirmation that what was obtained represent the objective reality. That means that in the alternative laboratory one should be able to reproduce the entire picture of the extended object obtained previously. Once again, the identification may be performed only by using the statistical methods of the data processing. I feel here a deep natural connection with the C.E.Shannon theory of communication but I am not prepared enough to enter into discussion.

Zbyszek:” I didn't see what is so spectacular in the Tonomura's experiment that could have force someone to take an orthodox point of view on QM.”

A.Tonomura experiment demonstrated the power of the human intellect which turns out to be able to extract the precise and detailed knowledge of what happens at electron Compton wave length distances.
Apparently, Born interpretation states that quantum physics may be treated only in terms of “potential reality”. From A.Tonomura experiment follows that one do not need any imagination. Everybody simply see the same picture.

 

[reilly]

Quote:
Originally Posted by reilly View PostYes, but. You suggest that the wall and slit boundaries have an important dynamical role in the double slit experiment. That's not so clear. Don't see many backscattered electrons from the slits.#1
Look at the physics: as an electron goes through a slit, it forces electrons in the wall away from the slit boundary. Both the electrons and nucleii are subject to thermal bouncing about. In my view, this is suficient to say that 1. the forces on a passing electron are small ( left balances right), and 2. average to zero over all but the shortest of times.

#1A
A somewhat more sophisticated approach is to treat the wall as composed of
nuclear-electron dipoles, which in turn are created by the fields of the passing electrons. This approach makes the handling of magnetism a bit easier.

The translation into QM is to get the "actual" potential seen by a passing electron, and include this in the Schrodinger Eq. (Not to worry about feedback of forces in this problem). Also a helpful fact: the dwell time of an electron in the wall's potential will generally be quite short.

Regards,
Reilly Atkinson

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>.
ueit
I think there is no doubt that the electron interacts with the slits, otherwise what part of the experiment is responsible for momentum conservation? The source? The detector?

The big question is how the interference fringes appear as a result of those interactions.

Regards,
Andrei Bocan
Report Post Reply With Quote

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>..
With all due respect, I find it hard to believe that you read my post. In fact, I provide an outline of how to compute the effects of of electron-screen interaction. (#1 and #1A) I will agree to laziness; I'm quite sure that this calculation has been done, but I will leave it at that.

For example; the Babinet opposite of the slit is simple, say, a "small" rectangular piece of screen material, or whatever. Scatter electrons from this target, and include the contribution of eddy currents, including polarization and magenetism. This could, for example, be of interest to users of electron microscopes.

Even if you can demonstrate that screen-electron interactions cause electron diffraction, you'll still have to worry about electron & neutron diffraction from crystal lattices. Tough job indeed.

Not to worry about momentum conservation: inspection of the system confirms that it's ok to treat the screen as if it has an infinite mass. That is it takes a huge hit to get the screen to move -- in comparison to an electron boucing from the screen.

Regards,
Reilly Atkinson

 

[zbyszek]

I tend to agree with you that QM is statistics, however, I have an objection to your argument.

The double slit experiment is explained using not pure QM but a semiclassical approximation of it. The electron is treated as a quantum, but the wall, source and detector not. In order to find out what QM really predicts for such an experiment we need a detailed description of the system, that is, the quantum state of the whole system. The result of such a ridiculously complex calculation could give you a much better prediction about the experimental outcome.

ueit,
This reply is late because I didn't notice that you actually referred to my post.

As a side note: the treatment I proposed is not semiclassical. The word semiclassical
usually means that some aspects of a dynamics of a system are treated classically rather
than quantally.
I propose to ignore the screen with the slits and the detector completely not just their quantum
nature. In their stead I recommend focusing on the wave function of the system of interest,
i.e. of the wave function of an electron just before it hits the detectors.

As you said, QM is statistics, so the wave function is just enough to generate outcomes
of an ideal experiment by sampling the corresponding probability density.

This way you escape from the measurement problem and from internal complexity of
the screen and the detectors.

Cheers!

 

[ueit]

Ah ? I certainly do. I think that Newtonian mechanics (points in 3-dim Euclidean space with forces and so on) and Lagrangian/Hamiltonian mechanics describe different ontologies ! (which are however observationally identical). In other words, when considering Hamiltonian mechanics, I *do* consider that its universe is a 6N dimensional tangent bundle and not a 3-dim Euclidean space, although one can find certainly a 3-dim Euclidean structure in there.

In order to calculate the Lagrangian we need potential and kinetic energies. I don't see the meaning of these parameters outside Newton's ontology. Once you use those parameters and everything else you need to calculate them (concepts like mass localized in 3d space, or force) it seems rather odd to claim that another ontology is at base.

A true example of a different ontology would be GR where the gravitational force is replaced with something else.

 

[vanesch]

In order to calculate the Lagrangian we need potential and kinetic energies. I don't see the meaning of these parameters outside Newton's ontology. Once you use those parameters and everything else you need to calculate them (concepts like mass localized in 3d space, or force) it seems rather odd to claim that another ontology is at base.

No, what I mean is that in a lagrangian formulation, the "world" is a single point in a configuration space, and not "multiple points in a 3-dim space". However, as you point out, the lagrangian "cost function" has strangely enough a special structure to it which links certain degrees of freedom with others in such a way as if they were points in a 3-dim space. It is this special structure of the lagrangian function which gives us then, in that single point in configuration space, an illusion of "multiple points in 3-dim space". So yes, in a certain way, there is a kind of "sub-structure" in the langrangian formulation which makes the dynamics in configuration space behave equivalently to a Newtonian formulation in 3 dim space. But this doesn't need to be the case, a priori, in a Lagrangian formulation. In principle, if the manifold of generalized coordinates is given, and a function L(q,q-dot) is given, that's all you need for a "lagrangian universe". Whether or not these q can be functions of a set of points in 3-dim euclidean space is something extra. It is this special structure which gives, to a creature living in a "lagrangian universe" the impression of living in a 3-dim euclidean space.

 

[ueit]

You mean that psi is then the summary of the interaction with the rest of the universe ? The "noise that comes from elsewhere" ?

Ok, but I can think of a toy universe just with one molecule in it, and I give it a certain quantum state |psi> which can be just any state (not even a stationary state). Clearly, this is then the "state of the universe" as there isn't anything else around. I can also give you the initial positions and velocities of the electrons and nucleae. And you can STILL not calculate the quantum forces without using psi - nevertheless, there is no "noise coming from elsewhere".

I only say that to show you that in BM, the wavefunction has a life of its own, with its own dynamics, and its own dynamical content which is NOT derivable from the particle positions and velocities elsewhere. As such, it is entirely part of the dynamical description, and hence must have its own ontology in addition to that of the particles.

Let's say that a universe consists of a single hydrogen atom with the electron in a p orbital. Now, for that universe, that's the only state it can be in. There is no way it can decay to a lower energy state. If a correct quantum theory for that universe exists, it has to predict with certainty its state (p), as any other state has to have 0 probability. Therefore BM doesn't need a separate ontology.

MWI is only a way of looking upon a quantum theory, and a quantum theory needs as its inputs the list of the degrees of freedom, the hamiltonian flow, and the link to (subjective) observation. Depending on that, you can put in the 3-dim space rather explicitly (such as is done in non-relativistic quantum mechanics or QFT), or you can hope that it will somehow emerge if you set up a different structure (LQG ?).

Is it not that structure you have to put by hand that defines the ontology?

P.S.

Can you point me, please, to an article containing a clear formulation of MWI in terms of its postulates?

 

[vanesch]

Can you point me, please, to an article containing a clear formulation of MWI in terms of its postulates?

http://plato.stanford.edu/entries/qm-manyworlds/

 

[ueit]

http://plato.stanford.edu/entries/qm-manyworlds/

Thanks.

Although all worlds are of the same physical size (this might not be true if we take quantum gravity into account), and in every world sentient beings feel as "real" as in any other world, in some sense some worlds are larger than others. I describe this property as the measure of existence of a world.[5] The measure of existence of a world quantifies its ability to interfere with other worlds in a gedanken experiment, see Vaidman 1998 (p. 256), and is the basis for introducing probability in the MWI. The measure of existence makes precise what is meant by the probability measure discussed in Everett 1957 and pictorially described in Lockwood 1989 (p. 230).

Is this "measure of existence" deduced somehow or postulated to be identical with Born's rule?

 

[vanesch]

Is this "measure of existence" deduced somehow or postulated to be identical with Born's rule?

That's the big question in MWI. Personally, I think you have to postulate it, and I even think I have the proof that it is logically independent. But some people try to deduce it. They are encouraged by that by things such as Gleason's theorem and similar results which indicate that (with some weak additional assumptions) the only consistent way of assigning probabilities to terms in a wavefunction is through the Born rule (the Hilbert norm in fact).

Personally, I don't think it is a problem that this is an extra postulate, because after all, it is part of the link between the "objective universe state" and the subjective "world experience" which is in any case, in this setting, a postulated relationship.

 

[ueit]

With all due respect, I find it hard to believe that you read my post. In fact, I provide an outline of how to compute the effects of of electron-screen interaction. (#1 and #1A) I will agree to laziness; I'm quite sure that this calculation has been done, but I will leave it at that.

I've certainly read your post. I may be a little lazy but the reasons for not doing the calculations you suggested are:

1. I have little time (full time job + 1 little kid) and I've forgot much of the math required.

2. There is no chance to explain interference in this way because the pattern changes when we cover a slit. The force the electron "feels" at the slit should depend on the macroscopic structure of the wall so we need a much complicated calculation (including for example the lattice oscillations, which are a function of the wall shape).

Even if you can demonstrate that screen-electron interactions cause electron diffraction, you'll still have to worry about electron & neutron diffraction from crystal lattices. Tough job indeed.

What other possible explanation could be for the particle's change in momentum if not an interaction with the wall (crystal lattice, whatever)?

Not to worry about momentum conservation: inspection of the system confirms that it's ok to treat the screen as if it has an infinite mass. That is it takes a huge hit to get the screen to move -- in comparison to an electron boucing from the screen.

Sure, momentum conservation is only important to prove that there is interaction between the particles and the wall.

As a matter of fact, there is, I think, another factor that should be taken into account, the influence of the wall on the source, prior to the particle's emission. It's the only way we could explain EPR experiments in a local manner and this probably applies to the double-slit as well.

Regards,
Andrei Bocan

 

[ueit]

ueit,
This reply is late because I didn't notice that you actually referred to my post.

As a side note: the treatment I proposed is not semiclassical. The word semiclassical
usually means that some aspects of a dynamics of a system are treated classically rather
than quantally.
I propose to ignore the screen with the slits and the detector completely not just their quantum
nature. In their stead I recommend focusing on the wave function of the system of interest,
i.e. of the wave function of an electron just before it hits the detectors.

As you said, QM is statistics, so the wave function is just enough to generate outcomes
of an ideal experiment by sampling the corresponding probability density.

This way you escape from the measurement problem and from internal complexity of
the screen and the detectors.

Cheers!

If the source is not known in detail you don't know the electron's original wave function.

If the wall is not known in detail you don't know the electron's wave function before the detector.

If the detector is not known in detail you cannot know where the spot is produced.

I'm not even sure that we can speak about the electron's wave function as it is probably entangled with both the source and the wall.

 

[zbyszek]

If the source is not known in detail you don't know the electron's original wave function.

If the wall is not known in detail you don't know the electron's wave function before the detector.

If the detector is not known in detail you cannot know where the spot is produced.

I'm not even sure that we can speak about the electron's wave function as it is probably entangled with both the source and the wall.

You can postulate what the reasonable electron w.f. is. And this is how it is done.

Notice, that if one has a problem with guessing the electron's w.f. then somewhat bigger
issue arises if it comes to the w.f.s of the detectors, walls, etc.. There, one
has to deal with 10^25 or more atoms. How do you propose to determine details of w.f.
for those objects?

The only realistic way is to guess their wave functions.

Why bother then? Since heavy guessing is inevitable, why not to guess just the electron w.f. and focus on its properties?

Otherwise you fall into a circular reasoning:
1. To determine w.f. of an object you have to measure it.
2. You don't know what you measure if you don't know the w.f. of the measuring
apparatus.
3. So, you have to measure the w.f. of the measuring apparatus, and so on ...

I propose to cut this circle in the most convenient point i.e. the one that requires
the least amount of guessing.

Would gladly hear about another way out, though.

Cheers!

 

[ueit]

You can postulate what the reasonable electron w.f. is. And this is how it is done.

Notice, that if one has a problem with guessing the electron's w.f. then somewhat bigger
issue arises if it comes to the w.f.s of the detectors, walls, etc.. There, one
has to deal with 10^25 or more atoms. How do you propose to determine details of w.f.
for those objects?

The only realistic way is to guess their wave functions.

Why bother then? Since heavy guessing is inevitable, why not to guess just the electron w.f. and focus on its properties?

Otherwise you fall into a circular reasoning:
1. To determine w.f. of an object you have to measure it.
2. You don't know what you measure if you don't know the w.f. of the measuring
apparatus.
3. So, you have to measure the w.f. of the measuring apparatus, and so on ...

I propose to cut this circle in the most convenient point i.e. the one that requires
the least amount of guessing.

If you want to test the statistical character of QM’s formalism you cannot use statistics in doing the calculations, that's fallacious. At least you should estimate the errors introduced at each step.

If, for practical reasons, you cannot calculate anything without statistics that only means that the problem remains open for debate, not that you are right.

I have an idea of how to do a full QM calculation:

1. Use an as small as possible system (a single anion as the source, a molecule as beam splitter, a few cations as the detector.

2. Use a computer simulation, not a real experiment; use the wave function of the whole system.

3. Visualize the experiment evolving in time for different initial parameters, using perhaps Bohm's approach.

4. See if some interesting correlations appear (for example between the detector's state before the electron's emission, and the detection event).

This way we could see QM's true predictive power as far as this experiment is concerned.

Cheers!

 

[zbyszek]

If you want to test the statistical character of QM’s formalism you cannot use statistics in doing the calculations, that's fallacious.

You are right. If I wanted the test that would stupid.

I have an idea of how to do a full QM calculation:

1. Use an as small as possible system (a single anion as the source, a molecule as beam splitter, a few cations as the detector.

2. Use a computer simulation, not a real experiment; use the wave function of the whole system.

3. Visualize the experiment evolving in time for different initial parameters, using perhaps Bohm's approach.

4. See if some interesting correlations appear (for example between the detector's state before the electron's emission, and the detection event).

This way we could see QM's true predictive power as far as this experiment is concerned.

I do similar simulations on the daily basis. Without calculating Bohm's trajectories,
because they do not provide any additional information.
What I have is the full evolution of many-body wave functions for systems with interacting
particles and for different initial wave functions.

What I get at the end of the evolution is another many body wave function. And this
is it for quantum mechanics.

The next step is to take the wave function modulus squared and sample it to generate possible
outcomes of a single run of the experiment.

Sometimes the structure of the wave function is such that only very limited class of single
run outcomes is possible, and they are observed in real life experiments. Mainly with condensates.


Cheers!

 

[reilly]

Reilly:...”

You consider only one aspect of the problem. Your description of the measurements fit perfectly the mathematical framework used in the classical physics. It essential feature is the use of analysis (classical,vector and tensor consequently). In the foundation of the analysis lies lim operation which can’t be reduced to addition and multiplication. It means intrinsically that for every predefined epsilon > 0 you may find suitable delta > 0. And thus your notion of accuracy fit it perfectly too.
However, QM do not follow that scenario.
Consider properly calibrated and functioning set of the measurement instruments. You perform the observation and obtain a point. Now you repeat the procedure for the identical system (the standard QM treatment of that notion). Your new observation is legal exactly as the previous. However, it do not always satisfy your requirement. Sometimes one obtain points where delta is arbitrary large. This do not mean that now your measurement equipment is spoiled. This mean that you met new physics (and new mathematics consequently).
Quantum world is not a classical world.

After spending time moving lead bricks around for shielding for electron scattering experiments, and working extensively with data from such experiments, I'll claim that the measurements don't know from quantum or classical. It's all in the eye of the beholder. Perhaps it's not quite a mantra, but "experiments are experiments", and "propagation of errors is propagation of errors." There's nothing quite like computing or measuring the 5th decimal place; tends to make one practical.

Regards,
Reilly Atkinson